I have to find the inverse function of f(x)=3-4x. I got y=3-x/4 for the function. I then have to plug it back into the function and verify that it is the inverse. So I wrote (3-4(3-x))/4. This resulted in (-3+x)/4=x. I tried isolating it to get x=x but I just can't get it. Where did I goof up?
if g(x) is the inverse of f(x), then
f(g(x)) should equal x.
You proved that....
f(inverse)=(3-4(3-x))/4=x
To find the inverse function of f(x), you correctly started by solving the equation y = 3 - x/4 for x in terms of y. However, it seems there was a mistake when plugging it back into the original function.
Let's go through the process again step by step:
1. Start with the equation y = 3 - x/4.
2. Swap the roles of x and y to get x = 3 - y/4.
3. To solve for y, we can multiply both sides of the equation by 4 to eliminate the fraction: 4x = 12 - y.
4. Next, rearrange the equation to isolate y by subtracting 12 from both sides: y = 12 - 4x.
Now, we have found the expression for the inverse function, which is y = 12 - 4x.
To verify that this is the inverse of f(x) = 3 - 4x:
1. Start with the original function f(x) = 3 - 4x.
2. Replace f(x) with y: y = 3 - 4x.
3. Replace x with the expression for the inverse function: y = 3 - 4(12 - 4x).
4. Distribute the -4 to both terms inside the parentheses: y = 3 - 48 + 16x.
5. Simplify the expression: y = -45 + 16x.
Comparing this with the original expression for the inverse function, y = 12 - 4x, we can see that these two functions are not equal.
Therefore, it seems there was an error in the plugging-back step, resulting in a different expression for the inverse function.